Question 3. [4 + 2 = 6 marks] Given the triple Zx 3Z, +, defined in...

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Question 3. [4 + 2 = 6 marks] Given the triple Zx 3Z, +, defined in terms of the Cartesian product Z x 3Z of two rings Z, and 3Z under operations (k, 3m) + (1, 3n) = (k+1,3m + 3n) and (k, 3m) (1, 3n) = (kl, 9mn) for k, l, m, n € Z. . (a) Prove that Zx 3Z, +, is a ring. Is it a commutative ring? Justify your answer. (b) Does the triple Zx 3Z, +, > form an integral domain? Justify your answer. . Question 3. [4 + 2 = 6 marks] Given the triple Zx 3Z, +, defined in terms of the Cartesian product Z x 3Z of two rings Z, and 3Z under operations (k, 3m) + (1, 3n) = (k+1,3m + 3n) and (k, 3m) (1, 3n) = (kl, 9mn) for k, l, m, n € Z. . (a) Prove that Zx 3Z, +, is a ring. Is it a commutative ring? Justify your answer. (b) Does the triple Zx 3Z, +, > form an integral domain? Justify your answer. .

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Let R be a ring with an identity An element a ER is a zero divisor if a0 and there exists b t... View the full answer